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Of lice and math: using models to understand and control populations of head lice.

Laguna MF, Laguna MF, Risau-Gusman S - PLoS ONE (2011)

Bottom Line: In the case of treatments, we study the difference in performance that arises when they are applied in systematic and non-systematic ways.It is shown that this parameter can be tuned to obtain collective infestations whose characteristics are compatible with what is given in the literature on real infestations.For both cases we assess the impact of several collective strategies of treatment.

View Article: PubMed Central - PubMed

Affiliation: Consejo Nacional de Investigaciones Cientficas y Técnicas and Centro Atómico Bariloche, Bariloche, Río Negro, Argentina. lagunaf@cab.cnea.gov.ar

ABSTRACT
In this paper we use detailed data about the biology of the head louse (pediculus humanus capitis) to build a model of the evolution of head lice colonies. Using theory and computer simulations, we show that the model can be used to assess the impact of the various strategies usually applied to eradicate head lice, both conscious (treatments) and unconscious (grooming). In the case of treatments, we study the difference in performance that arises when they are applied in systematic and non-systematic ways. Using some reasonable simplifying assumptions (as random mixing of human groups and the same mobility for all life stages of head lice other than eggs) we model the contagion of pediculosis using only one additional parameter. It is shown that this parameter can be tuned to obtain collective infestations whose characteristics are compatible with what is given in the literature on real infestations. We analyze two scenarios: One where group members begin treatment when a similar number of lice are present in each head, and another where there is one individual who starts treatment with a much larger threshold ("superspreader"). For both cases we assess the impact of several collective strategies of treatment.

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Related in: MedlinePlus

Performance of different treatments in a group of 3 heads.Duration of the infestation as a function of the efficacy of each application for a systematic treatment applied every 4 days, implemented in a synchronized (open symbols) and unsynchronized way (full symbols). Different curves correspond to different values of the transmission probability . For the unsynchronized case we have used scenario 1.
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pone-0021848-g010: Performance of different treatments in a group of 3 heads.Duration of the infestation as a function of the efficacy of each application for a systematic treatment applied every 4 days, implemented in a synchronized (open symbols) and unsynchronized way (full symbols). Different curves correspond to different values of the transmission probability . For the unsynchronized case we have used scenario 1.

Mentions: We have used our model to assess the performance of different treatments in a group of 3 heads (Fig. 10) and in a group of 20 heads (Fig. 11) with four different transmission probabilities . We have chosen a systematic treatment applied every 4 days with an efficacy per application of . We compare the durations of the collective infestation of the synchronized case and the unsynchronized case in scenario 1. The figures show that in this last case the duration of the treatment is multiplied by a number independent of the efficacy (at least in the range of efficacies shown), and this constant gets larger as is increased. Intuitively, the picture is clear: some lice manage to avoid the application of the remedy by jumping from one head to another, and this gets worse with more mobile lice and larger groups of heads. On the other hand, when the treatment is applied at the same moment in the whole group of heads there is almost no dependence on the rate of transmission, because jumping from head to head does not help lice to avoid the treatment. But the model allows us to go beyond intuitive arguments and to quantify these effects. For instance, Figs. 10 and 11 show that for the lack of synchronization increases the duration of the infestation of 3 heads by almost 50%, whereas for a group of 20 heads lack of synchronization almost doubles the duration of the infestation. It must be stressed that we are comparing with scenario 1, which lacks superspreaders. If these are included, the effect of synchronization is much more dramatic. To have an idea of the ‘perceived’ duration of the infestation one must subtract the time it takes the population of lice to achieve the detection threshold, which is approximately 3 weeks (see inset of Fig. 3).


Of lice and math: using models to understand and control populations of head lice.

Laguna MF, Laguna MF, Risau-Gusman S - PLoS ONE (2011)

Performance of different treatments in a group of 3 heads.Duration of the infestation as a function of the efficacy of each application for a systematic treatment applied every 4 days, implemented in a synchronized (open symbols) and unsynchronized way (full symbols). Different curves correspond to different values of the transmission probability . For the unsynchronized case we have used scenario 1.
© Copyright Policy
Related In: Results  -  Collection

Show All Figures
getmorefigures.php?uid=PMC3140471&req=5

pone-0021848-g010: Performance of different treatments in a group of 3 heads.Duration of the infestation as a function of the efficacy of each application for a systematic treatment applied every 4 days, implemented in a synchronized (open symbols) and unsynchronized way (full symbols). Different curves correspond to different values of the transmission probability . For the unsynchronized case we have used scenario 1.
Mentions: We have used our model to assess the performance of different treatments in a group of 3 heads (Fig. 10) and in a group of 20 heads (Fig. 11) with four different transmission probabilities . We have chosen a systematic treatment applied every 4 days with an efficacy per application of . We compare the durations of the collective infestation of the synchronized case and the unsynchronized case in scenario 1. The figures show that in this last case the duration of the treatment is multiplied by a number independent of the efficacy (at least in the range of efficacies shown), and this constant gets larger as is increased. Intuitively, the picture is clear: some lice manage to avoid the application of the remedy by jumping from one head to another, and this gets worse with more mobile lice and larger groups of heads. On the other hand, when the treatment is applied at the same moment in the whole group of heads there is almost no dependence on the rate of transmission, because jumping from head to head does not help lice to avoid the treatment. But the model allows us to go beyond intuitive arguments and to quantify these effects. For instance, Figs. 10 and 11 show that for the lack of synchronization increases the duration of the infestation of 3 heads by almost 50%, whereas for a group of 20 heads lack of synchronization almost doubles the duration of the infestation. It must be stressed that we are comparing with scenario 1, which lacks superspreaders. If these are included, the effect of synchronization is much more dramatic. To have an idea of the ‘perceived’ duration of the infestation one must subtract the time it takes the population of lice to achieve the detection threshold, which is approximately 3 weeks (see inset of Fig. 3).

Bottom Line: In the case of treatments, we study the difference in performance that arises when they are applied in systematic and non-systematic ways.It is shown that this parameter can be tuned to obtain collective infestations whose characteristics are compatible with what is given in the literature on real infestations.For both cases we assess the impact of several collective strategies of treatment.

View Article: PubMed Central - PubMed

Affiliation: Consejo Nacional de Investigaciones Cientficas y Técnicas and Centro Atómico Bariloche, Bariloche, Río Negro, Argentina. lagunaf@cab.cnea.gov.ar

ABSTRACT
In this paper we use detailed data about the biology of the head louse (pediculus humanus capitis) to build a model of the evolution of head lice colonies. Using theory and computer simulations, we show that the model can be used to assess the impact of the various strategies usually applied to eradicate head lice, both conscious (treatments) and unconscious (grooming). In the case of treatments, we study the difference in performance that arises when they are applied in systematic and non-systematic ways. Using some reasonable simplifying assumptions (as random mixing of human groups and the same mobility for all life stages of head lice other than eggs) we model the contagion of pediculosis using only one additional parameter. It is shown that this parameter can be tuned to obtain collective infestations whose characteristics are compatible with what is given in the literature on real infestations. We analyze two scenarios: One where group members begin treatment when a similar number of lice are present in each head, and another where there is one individual who starts treatment with a much larger threshold ("superspreader"). For both cases we assess the impact of several collective strategies of treatment.

Show MeSH
Related in: MedlinePlus